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A clause <jats:italic>C<\/jats:italic> is syntactically semi-relevant, if it occurs in some refutation of <jats:italic>N<\/jats:italic>. While syntactic relevance coincides with satisfiability (if <jats:italic>C<\/jats:italic> is syntactically relevant then <jats:inline-formula><jats:alternatives><jats:tex-math>$$N\\setminus \\{C\\}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                    <mml:mrow>\n                      <mml:mi>N<\/mml:mi>\n                      <mml:mo>\\<\/mml:mo>\n                      <mml:mo>{<\/mml:mo>\n                      <mml:mi>C<\/mml:mi>\n                      <mml:mo>}<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is satisfiable), the semantic counterpart for syntactic semi-relevance was not known so far. Using the new notion of a <jats:italic>conflict literal<\/jats:italic> we show that for independent clause sets <jats:italic>N<\/jats:italic> a clause <jats:italic>C<\/jats:italic> is syntactically semi-relevant in the clause set <jats:italic>N<\/jats:italic> if and only if it adds to the number of conflict literals in <jats:italic>N<\/jats:italic>. A clause set is independent, if no clause out of the clause set is the consequence of different clauses from the clause set.<\/jats:p><jats:p>Furthermore, we relate the notion of relevance to that of a minimally unsatisfiable subset (MUS) of some independent clause set <jats:italic>N<\/jats:italic>. In propositional logic, a clause <jats:italic>C<\/jats:italic> is relevant if it occurs in all MUSes of some clause set <jats:italic>N<\/jats:italic> and semi-relevant if it occurs in some MUS. For first-order logic the characterization needs to be refined with respect to ground instances of <jats:italic>N<\/jats:italic> and <jats:italic>C<\/jats:italic>.<\/jats:p>","DOI":"10.1007\/978-3-031-10769-6_13","type":"book-chapter","created":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T01:02:56Z","timestamp":1659315776000},"page":"208-227","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Semantic Relevance"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5139-4503","authenticated-orcid":false,"given":"Fajar","family":"Haifani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6002-0458","authenticated-orcid":false,"given":"Christoph","family":"Weidenbach","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,8,1]]},"reference":[{"issue":"1","key":"13_CR1","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1093\/logcom\/exn058","volume":"20","author":"F Baader","year":"2010","unstructured":"Baader, F., Pe\u00f1aloza, R.: Axiom pinpointing in general tableaux. 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